Evaluate
\frac{129}{22}\approx 5.863636364
Factor
\frac{3 \cdot 43}{2 \cdot 11} = 5\frac{19}{22} = 5.863636363636363
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)129}\\\end{array}
Use the 1^{st} digit 1 from dividend 129
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)129}\\\end{array}
Since 1 is less than 22, use the next digit 2 from dividend 129 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)129}\\\end{array}
Use the 2^{nd} digit 2 from dividend 129
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)129}\\\end{array}
Since 12 is less than 22, use the next digit 9 from dividend 129 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)129}\\\end{array}
Use the 3^{rd} digit 9 from dividend 129
\begin{array}{l}\phantom{22)}005\phantom{6}\\22\overline{)129}\\\phantom{22)}\underline{\phantom{}110\phantom{}}\\\phantom{22)9}19\\\end{array}
Find closest multiple of 22 to 129. We see that 5 \times 22 = 110 is the nearest. Now subtract 110 from 129 to get reminder 19. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }19
Since 19 is less than 22, stop the division. The reminder is 19. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}